题型:解答题 题类:期中考试 难易度:较难
已知等差数列\(\left\{ {{a}_{n}} \right\}\)满足:\({{a}_{3}}=7,{{a}_{5}}+{{a}_{7}}=26\),\(\left\{ {{a}_{n}} \right\}\)的前\(n\)项和为\({{S}_{n}}\).
\((1)\)求\({{a}_{n}}\)及\({{S}_{n}}\);
\((2)\)令\({{b}_{n}}=\dfrac{1}{a_{n}^{2}-1}\left( n\in {{N}^{{*}}} \right)\),求数列\(\left\{ {{b}_{n}} \right\}\)的前\(n\)项和\({{T}_{n}}\).